Sizing steps in sloped pipe to eliminate expansion loops

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thearny2
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I am working on a system that requires expansion loops. I have located formulae on engineering toolbox.com and the spirax sarco website for determining the size of the loops required. So a 2m wide loop needs to be 4m tall, and I need one every 17m, roughly.

What I struggling to get my head around is if I am stepping my pipe down a hill, what size and how often do I need a step to negate the requirement for expansion loops altogether. For some reason my mind can't piece this together. Does anybody have a view on the relationship?

My other question is, my aforementioned references, whilst useful, are hardly rock solid. Does anybody have a suggestion for references with a more defined foundation?

All ideas appreciated.
 

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The formulas in Spirax Sarco are useful but very conservative.

A 90 deg step down a hill will not be as affective as a loop of course.

I am fortunate I have access to the Caesar pipe stress software for these things.

What is your operating temperature.
 
From 15 to ca. 300 degC. I think there is about 30 com expansion in 50 m. The question is how many loops of what size do I need.

I keep getting a 4m high by 2m wide loop (twice), which intuitively seems massive to me, or a number of smaller ones.